sustainability Article Evolution and Evaluation of the Guangzhou Metro Network Topology Based on an Integration of Complex Network Analysis and GIS Shaopei Chen and Dachang Zhuang * School of Public Administration, Guangdong University of Finance and Economics, Guangzhou 510320, China; [email protected] * Correspondence: [email protected] Received: 11 December 2019; Accepted: 9 January 2020; Published: 10 January 2020 Abstract: This paper takes the metro network of Guangzhou as a case study, and provides a quantitative analysis of the historical development of the network from 1999 to 2018. Particularly, the evolution of the topological structure of the Guangzhou Metro Network (GMN) is evaluated and characterized through the integration of geographic information system (GIS) and complex network analysis. The results show that: (1) The metro network of Guangzhou possesses the basic characteristics of small-world network, (2) with the development of GMN, the network complexity is increased and the spatial dispersion of the nodes tends to ease, but the average travel time and transfer rate continues to rise up, leading to the decreasing of the network transmission efficiency and the scattering of the nodes, (3) a good fault tolerance of the overall metro network of Guangzhou is revealed, but the spatial variance is observed, (4) the peak of degree centrality (DC) of the nodes is gradually moving northward along “Kecun Station–Guangzhou railway station–Jiahe Wanggang station”, while the peak of betweenness centrality (BC) is changing from “Kecun station” to “Jiahe Wanggang station”, and Jiahe Wanggang station has evolved into the most critical node in the current metro network of Guangzhou. In conclusion, this study should provide the scientific basis and significant decision-making support to the planning and operation management of GMN. Keywords: metro network; complex network; topological structure; statistical analysis; GIS 1. Introduction With the development of modern transportation technology, the emerging countries and their major cities all over the world are seeking a well-developed urban rail transit network system to alleviate the increasingly serious traffic problems, especially to optimize land use spatial structure and transport accessibility in the urban system [1–3]. In China, for example, since the city of Beijing became the first city to have a metro line in 1969, there are now 35 metropolises with a metro network with a total mileage of nearly 4600 km. Among them, the top three metropolises with the largest metro network mileage are Shanghai, Beijing, and Guangzhou. Since 1997, the Guangzhou Metro Network (GMN) has been developing rapidly, while the economy of the city has been booming continuously. Currently, the metro network system in Guangzhou is composed of 16 lines (service routes) and 218 stations. As an important part of the modern public transport service system, the urban metro network has many advantages, such as large traffic volume, high speed, long distance, less pollution, and intensive land use, compared with the conventional public transport modes, such as bus and tram. Certainly, achieving a reliable metro network structure and reasonable spatial network distribution pattern should play a significant role in improving the quality of urban public transport services and promoting the urban sustainable development, especially in a developing country context [4]. Sustainability 2020, 12, 538; doi:10.3390/su12020538 www.mdpi.com/journal/sustainability Sustainability 2020, 12, 538 2 of 18 With the development of network science theory in the field of transport study, the complex network theory has become an important tool for modeling and characterizing the transport network topology. In the context of complex network theory [5,6], more and more scholars build transport network models based on Space-L and Space-P by using the entities (such as stops) of a complex network system and the interaction or association between the entities (such as service routes). Moreover, the graph theory and statistical physics are applied to explore the statistical law of the geometric and topological property in a transport network [7–10], with an important aim of providing the scientific references and decision-making support to the transport network planning. At present, the complex network theory has evolved into a new and extensive scientific paradigm of network system analysis and design. Many studies have focused on the analysis of the complexity, characteristics, and topological properties of urban rail transit network, such as a metro network, mainly considering the following aspects: (1) Measuring and characterizing the statistical characteristics such as node degree distribution of an urban metro network, and verifying its “small world” or/and “scale-free” phenomenon [11–13], (2) according to the geographical spatial characteristics of a given urban rail transit network, the powerful spatial analysis tools, such as geography information system (GIS), are integrated into the complex network analysis to evaluate the spatial network topological structure [14,15], (3) through measuring and quantifying the key topological parameters, such as degree centrality (DC), betweenness centrality (BC), and clustering coefficient (CC), the statistical characteristics of nodes in network are assessed thoroughly [16–21], (4) discussing the dynamic characteristics or the emergence behavior of the whole metro network while it is changing (such as being attacked), including vulnerability, reliability, robustness, etc. [22–27], furthermore, implementing the comparison between the urban metro network complexity characteristics in different cities, and then investigating the topology and classification of the given networks [19,21,28,29]. In summary, the existing research has carried out a more in-depth study of the topology and complexity characteristics of the transportation network. Especially, under the support of GIS, which is one of the innovative approaches that characterize the spatial correlation between spatial entities [30,31], the complex network analysis for the spatial topological characteristics of the transportation network shows a more extensive prospect. However, the empirical analysis of the topology evolution of a given metro network in its complete growing period is less involved, making it difficult to recognize the characteristics and issues in each developmental stage during the growth of a network. In addition, as a typical real-life network, although the basic topological properties and characteristics of an urban metro network can be intuitively revealed through the complex network analysis, in the absence of time, distance, time of transfer or other network service information, it is hard to learn clearly about the performance of network service, especially under a specific topological structure. Indeed, for urban planners, how to improve the service level and quality of a transport network is a crucial issue in urban planning. Therefore, on the basis of the complex network theory, this paper introduces the time cost, time of transfer, and other information of the travel paths among metro stations, and then establishes origin–destination (OD) matrixes and weighted network models during the growth of the Guangzhou Metro Network. Based on the complexity analysis of GMN, furthermore, this paper focuses on evaluating and characterizing the evolution of the spatial network topology and related issues in different network development stages by integrating with GIS. This study would serve as the scientific basis and decision-making support for the planning and operation management of the Guangzhou Metro Network. 2. Methodology 2.1. Modeling of Urban Metro Network In the context of the network science theory, the modeling of an urban public transport network (such as a metro network) is generally implemented by using the methods of Space-L and Space-P. In the network modeling based on Space-L, a station is identified as one node in a network, while there Sustainability 2020, 12, 538 3 of 18 Sustainability 2020, 12, 538 3 of 18 is at least one service route (i.e., a metro line) between two adjacent nodes, these two nodes should be should be connected with an edge. As a network modeling of Space‐P, a station is also defined as one connected with an edge. As a network modeling of Space-P, a station is also defined as one node in a node in a network, if there is at least one direct route (without transfer) between any two nodes, there network, if there is at least one direct route (without transfer) between any two nodes, there is an edge is an edge between them. As shown in Figure 1, the actual shape of a public transport network is between them. As shown in Figure1, the actual shape of a public transport network is illustrated, and illustrated, and the corresponding network modeling based on Space‐L and Space‐P is also presented, the corresponding network modeling based on Space-L and Space-P is also presented, respectively. respectively. Obviously, the Space‐P network model is built on the service routes of a public transport Obviously, the Space-P network model is built on the service routes of a public transport network, network, and currently is widely applied to investigate the transportability between two nodes in a and currently is widely applied to investigate the transportability between two nodes in a network. network. Therefore, compared with the Space‐L model, the network structure modeling based on Therefore, compared with the Space-L model, the network structure modeling based on Space-P can Space‐P can more realistically reflect the service level and quality of an urban public transport more realistically reflect the service level and quality of an urban public transport network. network. A B C Line 1 A-B-E-F Line 2 C-B-E-F Line 3 D-B-F Line 4 A-B-F D E F (a) prototype of urban public transport network A B C A B C D E F D E F (b) Space-L network topology (c) Space- P network structure modelling topology structure modelling Figure 1. Public transport network modeling based on Space-L and Space-P.